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The striker has signed a two-year contract with his decade-long spell at City ending upon the expiry of his contract next month.
Barca said Aguero's buy-out clause had been set at 100 million euro (just over £86million).
City announced on March 29 that Aguero's contract would not be renewed and that his 10-year stint at the club would end this summer.
Aguero joined City from Atletico Madrid in 2011 and went on to score 260 goals for the club, none more important than the stoppage-time strike which sealed the 2012 Premier League title.
Aguero is expected to be the first of a number of arrivals at the Camp Nou this summer as new president Joan Laporta looks to revamp a squad that could only finish third in La Liga.
Aguero's City team-mate Eric Garcia has been heavily linked as a transfer target, as have Dutch duo Memphis Depay - formerly of Manchester United - and Georginio Wijnaldum, who is leaving Liverpool next month.